A Thermally Activated Drug Delivery System Based on a Thermoresponsive Polymer and a Cooling Device: A Theoretical Assessment

School of Mathematics,Statisticsand Applied Mathematics,National University of Ireland,Galway, University Road, Galway, IrelandMACSI, Department of Mathematicsand Statistics,University of Limerick, Limerick, Irelande-mail: tuoi.vo@ul.ie

Rongbing Yang

School of Chemistry,National University of Ireland,Galway, University Road, Galway, Irelande-mail: r.yang1@nuigalway.ie

Abstract

A mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delivery system. The delivery device consists of a cooling material coated by a drug-loaded thermoresponsive polymeric film. Drug release is initiated by remotely dropping the temperature of the cooling material sufficiently for the temperature throughout the polymer coating to drop below its volume phase transition temperature (VPTT), causing the polymer to swell and release the drug. Drug release switches off again when heat conduction from an external fluid medium raises the polymer temperature to above the VPTT causing the polymer to collapse. Candidate cooling mechanisms based on endothermic chemical reactions, the Peltier effect, and the magnetocaloric effect is considered. In the thin polymer film limit, the model provides an upper bound for the temperature the cooling material must be lowered for drug release to be initiated. Significantly, the model predicts that the duration a thin polymer will continue to release drug in a single cycle is proportional to the square of the thickness of the cooling material. It is found that the system may be realized for realistic parameter values and materials. A simple illustrative calculation incorporating the presence of a heat source is presented, and the results suggest that conduction due to the initial temperature difference between the water and the cooling material can make the dominant contribution to heat transfer in the polymer as it reheats to its VPTT.

Figures

A schematic representation of (a) the polymer coated cooling device, and (b) a slice of the cooling material, polymer, and water at time t = 0 in the semi-infinite domain -HM < x <∞. The complete system lies along the infinite domain -∞ < x <∞, but is symmetric about the centerline of the cooling material at x = − HM.

(a) The leading order temperature of the polymer as a function of time, TP0 (t), with copper being the cooling material. Here, the initial temperature of cooling device and water are TMi=32°C and TWi=37°C, respectively, and various cooling material thicknesses, 2HM, have been used, and (b) the leading order time it takes the polymer to heat back up to its VPTT as a function of TMi for various cooling material thicknesses. Here, the VPTT is TVPT = 35.5∘C, the initial temperature of the water is TWi=37°C, and plots for both copper and water being the cooling material are displayed.

Plots of the temperature at the polymer-water interface as a function of time for various ratios of the polymer thickness HP to half the cooling device thickness HM, with HM = 3 mm. The cooling material is water in (a), and copper in (b). The thermal diffusivity and conductivity chosen for the polymer are αP=1×10-7m2s-1 and kP=0.15 Jm-1K-1s-1, respectively. The initial temperature of the cooling device and the water are TMi=32°C and TWi=37°C, respectively.

Numerical solutions for the temperature at the polymer-water interface as a function of time, and for various separations HW between the polymer and a constant heat source held at 37∘C. The polymer is of thickness HP = 150 μm, and the cooling material is water of thickness HM = 3 mm. The thermal diffusivity and conductivity chosen for the polymer are αP=1×10-7m2s-1 and kP=0.15 Jm-1K-1s-1, respectively. The initial temperature of cooling device and water are TMi=32°C and TWi=37°C, respectively.

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